Preservation of dynamic properties in qualitative modeling frameworks for gene regulatory networks

Mathematical modeling often helps to provide a systems perspective on gene regulatory networks. In particular, qualitative approaches are useful when detailed kinetic information is lacking. Multiple methods have been developed that implement qualitative information in different ways, e.g., in purely discrete or hybrid discrete/continuous models. In this paper, we compare the discrete asynchronous logical modeling formalism for gene regulatory networks due to R. Thomas with piecewise affine differential equation models. We provide a local characterization of the qualitative dynamics of a piecewise affine differential equation model using the discrete dynamics of a corresponding Thomas model. Based on this result, we investigate the consistency of higher-level dynamical properties such as attractor characteristics and reachability. We show that although the two approaches are based on equivalent information, the resulting qualitative dynamics are different. In particular, the dynamics of the piecewise affine differential equation model is not a simple refinement of the dynamics of the Thomas model     

Inferring the perturbed microRNA regulatory networks from gene expression data using a network propagation based method

Background

MicroRNAs (miRNAs) are a class of endogenous small regulatory RNAs. Identifications of the dys-regulated or perturbed miRNAs and their key target genes are important for understanding the regulatory networks associated with the studied cellular processes. Several computational methods have been developed to infer the perturbed miRNA regulatory networks by integrating genome-wide gene expression data and sequence-based miRNA-target predictions. However, most of them only use the expression information of the miRNA direct targets, rarely considering the secondary effects of miRNA perturbation on the global gene regulatory networks.

Results

We proposed a network propagation based method to infer the perturbed miRNAs and their key target genes by integrating gene expressions and global gene regulatory network information. The method used random walk with restart in gene regulatory networks to model the network effects of the miRNA perturbation. Then, it evaluated the significance of the correlation between the network effects of the miRNA perturbation and the gene differential expression levels with a forward searching strategy. Results show that our method outperformed several compared methods in rediscovering the experimentally perturbed miRNAs in cancer cell lines. Then, we applied it on a gene expression dataset of colorectal cancer clinical patient samples and inferred the perturbed miRNA regulatory networks of colorectal cancer, including several known oncogenic or tumor-suppressive miRNAs, such as miR-17, miR-26 and miR-145.

Conclusions

Our network propagation based method takes advantage of the network effect of the miRNA perturbation on its target genes. It is a useful approach to infer the perturbed miRNAs and their key target genes associated with the studied biological processes using gene expression data.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-255) contains supplementary material, which is available to authorized users.     

Dynamical approaches to modeling developmental gene regulatory networks

The network of interacting regulatory signals within a cell comprises one of the most complex and powerful computational systems in biology. Gene regulatory networks (GRNs) play a key role in transforming the information encoded in a genome into morphological form. To achieve this feat, GRNs must respond to and integrate environmental signals with their internal dynamics in a robust and coordinated fashion. The highly dynamic nature of this process lends itself to interpretation and analysis in the language of dynamical models. Modeling provides a means of systematically untangling the complicated structure of GRNs, a framework within which to simulate the behavior of reconstructed systems and, in some cases, suites of analytic tools for exploring that behavior and its implications. This review provides a general background to the idea of treating a regulatory network as a dynamical system, and describes a variety of different approaches that have been taken to the dynamical modeling of GRNs. Birth Defects Research (Part C) 87:131–142, 2009. © 2009 Wiley‐Liss, Inc.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

Synthetic circuits reveal how mechanisms of gene regulatory networks constrain evolution

Phenotypic variation is the raw material of adaptive Darwinian evolution. The phenotypic variation found in organismal development is biased towards certain phenotypes, but the molecular mechanisms behind such biases are still poorly understood. Gene regulatory networks have been proposed as one cause of constrained phenotypic variation. However, most pertinent evidence is theoretical rather than experimental. Here, we study evolutionary biases in two synthetic gene regulatory circuits expressed in Escherichia coli that produce a gene expression stripe—a pivotal pattern in embryonic development. The two parental circuits produce the same phenotype, but create it through different regulatory mechanisms. We show that mutations cause distinct novel phenotypes in the two networks and use a combination of experimental measurements, mathematical modelling and DNA sequencing to understand why mutations bring forth only some but not other novel gene expression phenotypes. Our results reveal that the regulatory mechanisms of networks restrict the possible phenotypic variation upon mutation. Consequently, seemingly equivalent networks can indeed be distinct in how they constrain the outcome of further evolution.     

Exact reconstruction of gene regulatory networks using compressive sensing

Background

We consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network’s sparseness.

Results

For the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.

Conclusions

The method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0400-4) contains supplementary material, which is available to authorized users.     

Graphical modeling for gene set analysis: A critical appraisal

Current demand for understanding the behavior of groups of related genes, combined with the greater availability of data, has led to an increased focus on statistical methods in gene set analysis. In this paper, we aim to perform a critical appraisal of the methodology based on graphical models developed in Massa et al. ( 2010 ) that uses pathway signaling networks as a starting point to develop statistically sound procedures for gene set analysis. We pay attention to the potential of the methodology with respect to the organizational aspects of dealing with such complex but highly informative starting structures, that is pathways. We focus on three themes: the translation of a biological pathway into a graph suitable for modeling, the role of shrinkage when more genes than samples are obtained, the evaluation of respondence of the statistical models to the biological expectations. To study the impact of shrinkage, two simulation studies will be run. To evaluate the biological expectation we will use data from a network with known behavior that offer the possibility of carrying out a realistic check of respondence of the model to changes in the experimental conditions.     

Algebraic connectivity may explain the evolution of gene regulatory networks

Gene expression is a result of the interplay between the structure, type, kinetics, and specificity of gene regulatory interactions, whose diversity gives rise to the variety of life forms. As the dynamic behavior of gene regulatory networks depends on their structure, here we attempt to determine structural reasons which, despite the similarities in global network properties, may explain the large differences in organismal complexity. We demonstrate that the algebraic connectivity, the smallest non-trivial eigenvalue of the Laplacian, of the directed gene regulatory networks decreases with the increase of organismal complexity, and may therefore explain the difference between the variety of analyzed regulatory networks. In addition, our results point out that, for the species considered in this study, evolution favours decreasing concentration of strategically positioned feed forward loops, so that the network as a whole can increase the specificity towards changing environments. Moreover, contrary to the existing results, we show that the average degree, the length of the longest cascade, and the average cascade length of gene regulatory networks cannot recover the evolutionary relationships between organisms. Whereas the dynamical properties of special subnetworks are relatively well understood, there is still limited knowledge about the evolutionary reasons for the already identified design principles pertaining to these special subnetworks, underlying the global quantitative features of gene regulatory networks of different organisms. The behavior of the algebraic connectivity, which we show valid on gene regulatory networks extracted from curated databases, can serve as an additional evolutionary principle of organism-specific regulatory networks.     

Reliability of regulatory networks and its evolution

The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the repressilator, we discuss concepts of reliability of rhythmic attractors. In a simple evolution process we investigate how overall network structure affects the reliability of the dynamics. In the course of the evolution, networks are selected for reliable dynamics. We find that most networks can be easily evolved towards reliable functioning while preserving the original function.     

Robustness and state-space structure of Boolean gene regulatory models

Robustness to perturbation is an important characteristic of genetic regulatory systems, but the relationship between robustness and model dynamics has not been clearly quantified. We propose a method for quantifying both robustness and dynamics in terms of state-space structures, for Boolean models of genetic regulatory systems. By investigating existing models of the Drosophila melanogaster segment polarity network and the Saccharomyces cerevisiae cell-cycle network, we show that the structure of attractor basins can yield insight into the underlying decision making required of the system, and also the way in which the system maximises its robustness. In particular, gene networks implementing decisions based on a few genes have simple state-space structures, and their attractors are robust by virtue of their simplicity. Gene networks with decisions that involve many interacting genes have correspondingly more complicated state-space structures, and robustness cannot be achieved through the structure of the attractor basins, but is achieved by larger attractor basins that dominate the state space. These different types of robustness are demonstrated by the two models: the D. melanogaster segment polarity network is robust due to simple attractor basins that implement decisions based on spatial signals; the S. cerevisiae cell-cycle network has a complicated state-space structure, and is robust only due to a giant attractor basin that dominates the state space.     

A cellular mechanism for multi-robot construction via evolutionary multi-objective optimization of a gene regulatory network

A major research challenge of multi-robot systems is to predict the emerging behaviors from the local interactions of the individual agents. Biological systems can generate robust and complex behaviors through relatively simple local interactions in a world characterized by rapid changes, high uncertainty, infinite richness, and limited availability of information. Gene Regulatory Networks (GRNs) play a central role in understanding natural evolution and development of biological organisms from cells. In this paper, inspired by biological organisms, we propose a distributed GRN-based algorithm for a multi-robot construction task. Through this algorithm, multiple robots can self-organize autonomously into different predefined shapes, and self-reorganize adaptively under dynamic environments. This developmental process is evolved using a multi-objective optimization algorithm to achieve a shorter travel distance and less convergence time. Furthermore, a theoretical proof of the system's convergence is also provided. Various case studies have been conducted in the simulation, and the results show the efficiency and convergence of the proposed method.